3 * Interface to GiNaC's light-weight expression handles. */
6 * GiNaC Copyright (C) 1999-2006 Johannes Gutenberg University Mainz, Germany
8 * This program is free software; you can redistribute it and/or modify
9 * it under the terms of the GNU General Public License as published by
10 * the Free Software Foundation; either version 2 of the License, or
11 * (at your option) any later version.
13 * This program is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 * GNU General Public License for more details.
18 * You should have received a copy of the GNU General Public License
19 * along with this program; if not, write to the Free Software
20 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
23 #ifndef __GINAC_EX_H__
24 #define __GINAC_EX_H__
37 /** Helper class to initialize the library. There must be one static object
38 * of this class in every object file that makes use of our flyweights in
39 * order to guarantee proper initialization. Hence we put it into this
40 * file which is included by every relevant file anyways. This is modeled
41 * after section 27.4.2.1.6 of the C++ standard, where cout and friends are
52 /** For construction of flyweights, etc. */
53 static library_init library_initializer;
55 /** Rotate bits of unsigned value by one bit to the left.
56 * This can be necesary if the user wants to define its own hashes. */
57 inline unsigned rotate_left(unsigned n)
59 return (n & 0x80000000U) ? (n << 1 | 0x00000001U) : (n << 1);
62 class scalar_products;
64 class const_preorder_iterator;
65 class const_postorder_iterator;
68 /** Lightweight wrapper for GiNaC's symbolic objects. It holds a pointer to
69 * the other object in order to do garbage collection by the method of
70 * reference counting. I.e., it is a smart pointer. Also, the constructor
71 * ex::ex(const basic & other) calls the methods that do automatic
72 * evaluation. E.g., x-x turns automatically into 0. */
74 friend class archive_node;
75 friend inline bool are_ex_trivially_equal(const ex &, const ex &);
76 template<class T> friend inline const T &ex_to(const ex &);
77 template<class T> friend inline bool is_a(const ex &);
78 template<class T> friend inline bool is_exactly_a(const ex &);
80 // default constructor, copy constructor and assignment operator
86 ex(const basic & other);
93 /** Construct ex from string and a list of symbols. The input grammar is
94 * similar to the GiNaC output format. All symbols and indices to be used
95 * in the expression must be specified in a lst in the second argument.
96 * Undefined symbols and other parser errors will throw an exception. */
97 ex(const std::string &s, const ex &l);
100 // non-virtual functions in this class
102 /** Efficiently swap the contents of two expressions. */
103 void swap(ex & other) throw()
105 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
106 GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
111 const_iterator begin() const throw();
112 const_iterator end() const throw();
113 const_preorder_iterator preorder_begin() const;
114 const_preorder_iterator preorder_end() const throw();
115 const_postorder_iterator postorder_begin() const;
116 const_postorder_iterator postorder_end() const throw();
119 ex eval(int level = 0) const { return bp->eval(level); }
120 ex evalf(int level = 0) const { return bp->evalf(level); }
121 ex evalm() const { return bp->evalm(); }
122 ex eval_ncmul(const exvector & v) const { return bp->eval_ncmul(v); }
123 ex eval_integ() const { return bp->eval_integ(); }
126 void print(const print_context & c, unsigned level = 0) const;
127 void dbgprint() const;
128 void dbgprinttree() const;
131 bool info(unsigned inf) const { return bp->info(inf); }
134 size_t nops() const { return bp->nops(); }
135 ex op(size_t i) const { return bp->op(i); }
136 ex operator[](const ex & index) const { return (*bp)[index]; }
137 ex operator[](size_t i) const { return (*bp)[i]; }
138 ex & let_op(size_t i);
139 ex & operator[](const ex & index);
140 ex & operator[](size_t i);
144 // function for complex expressions
145 ex conjugate() const { return bp->conjugate(); }
146 ex real_part() const { return bp->real_part(); }
147 ex imag_part() const { return bp->imag_part(); }
150 bool has(const ex & pattern, unsigned options = 0) const { return bp->has(pattern, options); }
151 bool find(const ex & pattern, lst & found) const;
152 bool match(const ex & pattern) const;
153 bool match(const ex & pattern, lst & repl_lst) const { return bp->match(pattern, repl_lst); }
156 ex subs(const exmap & m, unsigned options = 0) const;
157 ex subs(const lst & ls, const lst & lr, unsigned options = 0) const;
158 ex subs(const ex & e, unsigned options = 0) const;
161 ex map(map_function & f) const { return bp->map(f); }
162 ex map(ex (*f)(const ex & e)) const;
164 // visitors and tree traversal
165 void accept(visitor & v) const { bp->accept(v); }
166 void traverse_preorder(visitor & v) const;
167 void traverse_postorder(visitor & v) const;
168 void traverse(visitor & v) const { traverse_preorder(v); }
171 bool is_polynomial(const ex & vars) const;
172 int degree(const ex & s) const { return bp->degree(s); }
173 int ldegree(const ex & s) const { return bp->ldegree(s); }
174 ex coeff(const ex & s, int n = 1) const { return bp->coeff(s, n); }
175 ex lcoeff(const ex & s) const { return coeff(s, degree(s)); }
176 ex tcoeff(const ex & s) const { return coeff(s, ldegree(s)); }
179 ex expand(unsigned options=0) const;
180 ex collect(const ex & s, bool distributed = false) const { return bp->collect(s, distributed); }
182 // differentiation and series expansion
183 ex diff(const symbol & s, unsigned nth = 1) const;
184 ex series(const ex & r, int order, unsigned options = 0) const;
186 // rational functions
187 ex normal(int level = 0) const;
188 ex to_rational(exmap & repl) const;
189 ex to_rational(lst & repl_lst) const;
190 ex to_polynomial(exmap & repl) const;
191 ex to_polynomial(lst & repl_lst) const;
194 ex numer_denom() const;
196 // polynomial algorithms
197 ex unit(const ex &x) const;
198 ex content(const ex &x) const;
199 numeric integer_content() const;
200 ex primpart(const ex &x) const;
201 ex primpart(const ex &x, const ex &cont) const;
202 void unitcontprim(const ex &x, ex &u, ex &c, ex &p) const;
203 ex smod(const numeric &xi) const { return bp->smod(xi); }
204 numeric max_coefficient() const;
207 exvector get_free_indices() const { return bp->get_free_indices(); }
208 ex simplify_indexed(unsigned options = 0) const;
209 ex simplify_indexed(const scalar_products & sp, unsigned options = 0) const;
212 int compare(const ex & other) const;
213 bool is_equal(const ex & other) const;
214 bool is_zero() const { extern const ex _ex0; return is_equal(_ex0); }
215 bool is_zero_matrix() const;
218 ex symmetrize() const;
219 ex symmetrize(const lst & l) const;
220 ex antisymmetrize() const;
221 ex antisymmetrize(const lst & l) const;
222 ex symmetrize_cyclic() const;
223 ex symmetrize_cyclic(const lst & l) const;
226 unsigned return_type() const { return bp->return_type(); }
227 tinfo_t return_type_tinfo() const { return bp->return_type_tinfo(); }
229 unsigned gethash() const { return bp->gethash(); }
232 static ptr<basic> construct_from_basic(const basic & other);
233 static basic & construct_from_int(int i);
234 static basic & construct_from_uint(unsigned int i);
235 static basic & construct_from_long(long i);
236 static basic & construct_from_ulong(unsigned long i);
237 static basic & construct_from_double(double d);
238 static ptr<basic> construct_from_string_and_lst(const std::string &s, const ex &l);
239 void makewriteable();
240 void share(const ex & other) const;
245 mutable ptr<basic> bp; ///< pointer to basic object managed by this
249 // performance-critical inlined method implementations
251 // This needs to be a basic* because we don't know that numeric is derived
252 // from basic and we need a basic& for the ex default constructor
253 extern const basic *_num0_bp;
256 ex::ex() throw() : bp(*const_cast<basic *>(_num0_bp))
258 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
262 ex::ex(const basic & other) : bp(construct_from_basic(other))
264 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
268 ex::ex(int i) : bp(construct_from_int(i))
270 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
274 ex::ex(unsigned int i) : bp(construct_from_uint(i))
276 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
280 ex::ex(long i) : bp(construct_from_long(i))
282 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
286 ex::ex(unsigned long i) : bp(construct_from_ulong(i))
288 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
292 ex::ex(double const d) : bp(construct_from_double(d))
294 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
298 ex::ex(const std::string &s, const ex &l) : bp(construct_from_string_and_lst(s, l))
300 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
304 int ex::compare(const ex & other) const
306 #ifdef GINAC_COMPARE_STATISTICS
307 compare_statistics.total_compares++;
309 if (bp == other.bp) // trivial case: both expressions point to same basic
311 #ifdef GINAC_COMPARE_STATISTICS
312 compare_statistics.nontrivial_compares++;
314 const int cmpval = bp->compare(*other.bp);
317 // Expressions point to different, but equal, trees: conserve
318 // memory and make subsequent compare() operations faster by
319 // making both expressions point to the same tree.
327 bool ex::is_equal(const ex & other) const
329 #ifdef GINAC_COMPARE_STATISTICS
330 compare_statistics.total_is_equals++;
332 if (bp == other.bp) // trivial case: both expressions point to same basic
334 #ifdef GINAC_COMPARE_STATISTICS
335 compare_statistics.nontrivial_is_equals++;
337 const bool equal = bp->is_equal(*other.bp);
340 // Expressions point to different, but equal, trees: conserve
341 // memory and make subsequent compare() operations faster by
342 // making both expressions point to the same tree.
352 class const_iterator : public std::iterator<std::random_access_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
354 friend class const_preorder_iterator;
355 friend class const_postorder_iterator;
358 const_iterator() throw() {}
361 const_iterator(const ex &e_, size_t i_) throw() : e(e_), i(i_) {}
364 // This should return an ex&, but that would be a reference to a
371 // This should return an ex*, but that would be a pointer to a
373 std::auto_ptr<ex> operator->() const
375 return std::auto_ptr<ex>(new ex(operator*()));
378 ex operator[](difference_type n) const
383 const_iterator &operator++() throw()
389 const_iterator operator++(int) throw()
391 const_iterator tmp = *this;
396 const_iterator &operator+=(difference_type n) throw()
402 const_iterator operator+(difference_type n) const throw()
404 return const_iterator(e, i + n);
407 inline friend const_iterator operator+(difference_type n, const const_iterator &it) throw()
409 return const_iterator(it.e, it.i + n);
412 const_iterator &operator--() throw()
418 const_iterator operator--(int) throw()
420 const_iterator tmp = *this;
425 const_iterator &operator-=(difference_type n) throw()
431 const_iterator operator-(difference_type n) const throw()
433 return const_iterator(e, i - n);
436 inline friend difference_type operator-(const const_iterator &lhs, const const_iterator &rhs) throw()
438 return lhs.i - rhs.i;
441 bool operator==(const const_iterator &other) const throw()
443 return are_ex_trivially_equal(e, other.e) && i == other.i;
446 bool operator!=(const const_iterator &other) const throw()
448 return !(*this == other);
451 bool operator<(const const_iterator &other) const throw()
456 bool operator>(const const_iterator &other) const throw()
458 return other < *this;
461 bool operator<=(const const_iterator &other) const throw()
463 return !(other < *this);
466 bool operator>=(const const_iterator &other) const throw()
468 return !(*this < other);
472 ex e; // this used to be a "const basic *", but in view of object fusion that wouldn't be safe
479 _iter_rep(const ex &e_, size_t i_, size_t i_end_) : e(e_), i(i_), i_end(i_end_) {}
481 bool operator==(const _iter_rep &other) const throw()
483 return are_ex_trivially_equal(e, other.e) && i == other.i;
486 bool operator!=(const _iter_rep &other) const throw()
488 return !(*this == other);
496 } // namespace internal
498 class const_preorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
500 const_preorder_iterator() throw() {}
502 const_preorder_iterator(const ex &e, size_t n)
504 s.push(internal::_iter_rep(e, 0, n));
508 reference operator*() const
513 pointer operator->() const
518 const_preorder_iterator &operator++()
524 const_preorder_iterator operator++(int)
526 const_preorder_iterator tmp = *this;
531 bool operator==(const const_preorder_iterator &other) const throw()
536 bool operator!=(const const_preorder_iterator &other) const throw()
538 return !(*this == other);
542 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
546 while (!s.empty() && s.top().i == s.top().i_end) {
553 internal::_iter_rep & current = s.top();
555 if (current.i != current.i_end) {
556 const ex & child = current.e.op(current.i);
557 s.push(internal::_iter_rep(child, 0, child.nops()));
562 class const_postorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
564 const_postorder_iterator() throw() {}
566 const_postorder_iterator(const ex &e, size_t n)
568 s.push(internal::_iter_rep(e, 0, n));
573 reference operator*() const
578 pointer operator->() const
583 const_postorder_iterator &operator++()
589 const_postorder_iterator operator++(int)
591 const_postorder_iterator tmp = *this;
596 bool operator==(const const_postorder_iterator &other) const throw()
601 bool operator!=(const const_postorder_iterator &other) const throw()
603 return !(*this == other);
607 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
611 while (s.top().i != s.top().i_end) {
612 internal::_iter_rep & current = s.top();
613 const ex & child = current.e.op(current.i);
614 s.push(internal::_iter_rep(child, 0, child.nops()));
620 if (s.top().i == s.top().i_end)
629 inline const_iterator ex::begin() const throw()
631 return const_iterator(*this, 0);
634 inline const_iterator ex::end() const throw()
636 return const_iterator(*this, nops());
639 inline const_preorder_iterator ex::preorder_begin() const
641 return const_preorder_iterator(*this, nops());
644 inline const_preorder_iterator ex::preorder_end() const throw()
646 return const_preorder_iterator();
649 inline const_postorder_iterator ex::postorder_begin() const
651 return const_postorder_iterator(*this, nops());
654 inline const_postorder_iterator ex::postorder_end() const throw()
656 return const_postorder_iterator();
662 /** Compare two objects of class quickly without doing a deep tree traversal.
663 * @return "true" if they are equal
664 * "false" if equality cannot be established quickly (e1 and e2 may
665 * still be equal, in this case. */
666 inline bool are_ex_trivially_equal(const ex &e1, const ex &e2)
668 return e1.bp == e2.bp;
671 /* Function objects for STL sort() etc. */
672 struct ex_is_less : public std::binary_function<ex, ex, bool> {
673 bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; }
676 struct ex_is_equal : public std::binary_function<ex, ex, bool> {
677 bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); }
680 struct op0_is_equal : public std::binary_function<ex, ex, bool> {
681 bool operator() (const ex &lh, const ex &rh) const { return lh.op(0).is_equal(rh.op(0)); }
684 struct ex_swap : public std::binary_function<ex, ex, void> {
685 void operator() (ex &lh, ex &rh) const { lh.swap(rh); }
688 // Make it possible to print exvectors and exmaps
689 std::ostream & operator<<(std::ostream & os, const exvector & e);
690 std::ostream & operator<<(std::ostream & os, const exset & e);
691 std::ostream & operator<<(std::ostream & os, const exmap & e);
693 // wrapper functions around member functions
694 inline size_t nops(const ex & thisex)
695 { return thisex.nops(); }
697 inline ex expand(const ex & thisex, unsigned options = 0)
698 { return thisex.expand(options); }
700 inline ex conjugate(const ex & thisex)
701 { return thisex.conjugate(); }
703 inline ex real_part(const ex & thisex)
704 { return thisex.real_part(); }
706 inline ex imag_part(const ex & thisex)
707 { return thisex.imag_part(); }
709 inline bool has(const ex & thisex, const ex & pattern, unsigned options = 0)
710 { return thisex.has(pattern, options); }
712 inline bool find(const ex & thisex, const ex & pattern, lst & found)
713 { return thisex.find(pattern, found); }
715 inline bool is_polynomial(const ex & thisex, const ex & vars)
716 { return thisex.is_polynomial(vars); }
718 inline int degree(const ex & thisex, const ex & s)
719 { return thisex.degree(s); }
721 inline int ldegree(const ex & thisex, const ex & s)
722 { return thisex.ldegree(s); }
724 inline ex coeff(const ex & thisex, const ex & s, int n=1)
725 { return thisex.coeff(s, n); }
727 inline ex numer(const ex & thisex)
728 { return thisex.numer(); }
730 inline ex denom(const ex & thisex)
731 { return thisex.denom(); }
733 inline ex numer_denom(const ex & thisex)
734 { return thisex.numer_denom(); }
736 inline ex normal(const ex & thisex, int level=0)
737 { return thisex.normal(level); }
739 inline ex to_rational(const ex & thisex, lst & repl_lst)
740 { return thisex.to_rational(repl_lst); }
742 inline ex to_rational(const ex & thisex, exmap & repl)
743 { return thisex.to_rational(repl); }
745 inline ex to_polynomial(const ex & thisex, exmap & repl)
746 { return thisex.to_polynomial(repl); }
748 inline ex to_polynomial(const ex & thisex, lst & repl_lst)
749 { return thisex.to_polynomial(repl_lst); }
751 inline ex collect(const ex & thisex, const ex & s, bool distributed = false)
752 { return thisex.collect(s, distributed); }
754 inline ex eval(const ex & thisex, int level = 0)
755 { return thisex.eval(level); }
757 inline ex evalf(const ex & thisex, int level = 0)
758 { return thisex.evalf(level); }
760 inline ex evalm(const ex & thisex)
761 { return thisex.evalm(); }
763 inline ex eval_integ(const ex & thisex)
764 { return thisex.eval_integ(); }
766 inline ex diff(const ex & thisex, const symbol & s, unsigned nth = 1)
767 { return thisex.diff(s, nth); }
769 inline ex series(const ex & thisex, const ex & r, int order, unsigned options = 0)
770 { return thisex.series(r, order, options); }
772 inline bool match(const ex & thisex, const ex & pattern, lst & repl_lst)
773 { return thisex.match(pattern, repl_lst); }
775 inline ex simplify_indexed(const ex & thisex, unsigned options = 0)
776 { return thisex.simplify_indexed(options); }
778 inline ex simplify_indexed(const ex & thisex, const scalar_products & sp, unsigned options = 0)
779 { return thisex.simplify_indexed(sp, options); }
781 inline ex symmetrize(const ex & thisex)
782 { return thisex.symmetrize(); }
784 inline ex symmetrize(const ex & thisex, const lst & l)
785 { return thisex.symmetrize(l); }
787 inline ex antisymmetrize(const ex & thisex)
788 { return thisex.antisymmetrize(); }
790 inline ex antisymmetrize(const ex & thisex, const lst & l)
791 { return thisex.antisymmetrize(l); }
793 inline ex symmetrize_cyclic(const ex & thisex)
794 { return thisex.symmetrize_cyclic(); }
796 inline ex symmetrize_cyclic(const ex & thisex, const lst & l)
797 { return thisex.symmetrize_cyclic(l); }
799 inline ex op(const ex & thisex, size_t i)
800 { return thisex.op(i); }
802 inline ex lhs(const ex & thisex)
803 { return thisex.lhs(); }
805 inline ex rhs(const ex & thisex)
806 { return thisex.rhs(); }
808 inline bool is_zero(const ex & thisex)
809 { return thisex.is_zero(); }
811 inline void swap(ex & e1, ex & e2)
814 inline ex ex::subs(const exmap & m, unsigned options) const
816 return bp->subs(m, options);
819 inline ex subs(const ex & thisex, const exmap & m, unsigned options = 0)
820 { return thisex.subs(m, options); }
822 inline ex subs(const ex & thisex, const lst & ls, const lst & lr, unsigned options = 0)
823 { return thisex.subs(ls, lr, options); }
825 inline ex subs(const ex & thisex, const ex & e, unsigned options = 0)
826 { return thisex.subs(e, options); }
829 /* Convert function pointer to function object suitable for map(). */
830 class pointer_to_map_function : public map_function {
832 ex (*ptr)(const ex &);
834 explicit pointer_to_map_function(ex x(const ex &)) : ptr(x) {}
835 ex operator()(const ex & e) { return ptr(e); }
839 class pointer_to_map_function_1arg : public map_function {
841 ex (*ptr)(const ex &, T1);
844 explicit pointer_to_map_function_1arg(ex x(const ex &, T1), T1 a1) : ptr(x), arg1(a1) {}
845 ex operator()(const ex & e) { return ptr(e, arg1); }
848 template<class T1, class T2>
849 class pointer_to_map_function_2args : public map_function {
851 ex (*ptr)(const ex &, T1, T2);
855 explicit pointer_to_map_function_2args(ex x(const ex &, T1, T2), T1 a1, T2 a2) : ptr(x), arg1(a1), arg2(a2) {}
856 ex operator()(const ex & e) { return ptr(e, arg1, arg2); }
859 template<class T1, class T2, class T3>
860 class pointer_to_map_function_3args : public map_function {
862 ex (*ptr)(const ex &, T1, T2, T3);
867 explicit pointer_to_map_function_3args(ex x(const ex &, T1, T2, T3), T1 a1, T2 a2, T3 a3) : ptr(x), arg1(a1), arg2(a2), arg3(a3) {}
868 ex operator()(const ex & e) { return ptr(e, arg1, arg2, arg3); }
872 class pointer_to_member_to_map_function : public map_function {
874 ex (C::*ptr)(const ex &);
877 explicit pointer_to_member_to_map_function(ex (C::*member)(const ex &), C &obj) : ptr(member), c(obj) {}
878 ex operator()(const ex & e) { return (c.*ptr)(e); }
881 template<class C, class T1>
882 class pointer_to_member_to_map_function_1arg : public map_function {
884 ex (C::*ptr)(const ex &, T1);
888 explicit pointer_to_member_to_map_function_1arg(ex (C::*member)(const ex &, T1), C &obj, T1 a1) : ptr(member), c(obj), arg1(a1) {}
889 ex operator()(const ex & e) { return (c.*ptr)(e, arg1); }
892 template<class C, class T1, class T2>
893 class pointer_to_member_to_map_function_2args : public map_function {
895 ex (C::*ptr)(const ex &, T1, T2);
900 explicit pointer_to_member_to_map_function_2args(ex (C::*member)(const ex&, T1, T2), C &obj, T1 a1, T2 a2) : ptr(member), c(obj), arg1(a1), arg2(a2) {}
901 ex operator()(const ex & e) { return (c.*ptr)(e, arg1, arg2); }
904 template<class C, class T1, class T2, class T3>
905 class pointer_to_member_to_map_function_3args : public map_function {
907 ex (C::*ptr)(const ex &, T1, T2, T3);
913 explicit pointer_to_member_to_map_function_3args(ex (C::*member)(const ex &, T1, T2, T3), C &obj, T1 a1, T2 a2, T3 a3) : ptr(member), c(obj), arg1(a1), arg2(a2), arg3(a3) {}
914 ex operator()(const ex & e) { return (c.*ptr)(e, arg1, arg2, arg3); }
917 inline ex ex::map(ex f(const ex &)) const
919 pointer_to_map_function fcn(f);
923 // convenience type checker template functions
925 /** Check if ex is a handle to a T, including base classes. */
927 inline bool is_a(const ex &obj)
929 return is_a<T>(*obj.bp);
932 /** Check if ex is a handle to a T, not including base classes. */
934 inline bool is_exactly_a(const ex &obj)
936 return is_exactly_a<T>(*obj.bp);
939 /** Return a reference to the basic-derived class T object embedded in an
940 * expression. This is fast but unsafe: the result is undefined if the
941 * expression does not contain a T object at its top level. Hence, you
942 * should generally check the type of e first. Also, you shouldn't cache
943 * the returned reference because GiNaC's garbage collector may destroy
944 * the referenced object any time it's used in another expression.
946 * @param e expression
947 * @return reference to object of class T
948 * @see is_exactly_a<class T>() */
950 inline const T &ex_to(const ex &e)
952 GINAC_ASSERT(is_a<T>(e));
953 return static_cast<const T &>(*e.bp);
959 // Specializations of Standard Library algorithms
962 /** Specialization of std::swap() for ex objects. */
964 inline void swap(GiNaC::ex &a, GiNaC::ex &b)
969 /** Specialization of std::iter_swap() for vector<ex> iterators. */
971 inline void iter_swap(vector<GiNaC::ex>::iterator i1, vector<GiNaC::ex>::iterator i2)
976 /** Specialization of std::iter_swap() for list<ex> iterators. */
978 inline void iter_swap(list<GiNaC::ex>::iterator i1, list<GiNaC::ex>::iterator i2)
985 #endif // ndef __GINAC_EX_H__